Kinetic studies of base-catalyzed transesterification reactions of non-edible oils to prepare biodiesel: The effect of Co-solvent and temperature
The non-edible oils of mahua and jatropha were transesterified using methanol and 1 wt % KOH as the catalyst. The effect of co-solvent and the kinetic study of the transesterification of mahua oil is being reported here for the first time. Kinetics, modeled as a single-step reaction, revealed that the order of the reaction is 2 with respect to the triglyceride concentration and 1 with respect to the methanol concentration in both oils. In the presence of co-solvent, tetrahydrofuran (THF), methanolysis of mahua oil resulted in the increase of the rate constants from 0.08 to 1.17 L2 mol-2 min-1 at 28 °C and from 0.43 to 3.18 L2 mol -2 min-1 at 45 °C. The corresponding values for jatropha oil were found to be 0.50 and 2.76 L2 mol-2 min-1 at 28 °C and 1.26 and 4.56 L2 mol-2 min-1 at 45 °C. © 2011 American Chemical Society.
The Gibbs-Duhem equation, the ideal gas mixture, and a generalized interpretation of Daltons Law
The ideas used by Gibbs in defining the ideal gas mixture are brought to light in view of their fundamental significance and the fact that they have not received due attention in the literature. Specifically, the central role played by the well-known Gibbs-Duhem equation in this regard is explained. The concept of a fundamental equation and its importance in the definition of an ideal gas as well as an ideal gas mixture is elucidated. The manner in which these ideas enabled Gibbs to give a very general interpretation of Daltons law is examined in detail. © 2011 American Chemical Society.
Phase rule and the azeotrope - A critique and a new interpretation
The differences between the modern version of the phase rule and the one originally proposed by Gibbs are pointed out. The local analysis implied in Gibbs's approach to the phase rule is carried forward to its logical conclusion using the implicit function theorem. The results of the analysis are used to resolve the apparent contradictions in the interpretation of the phase rule, using the Gibbs-Duhem equations, for a system exhibiting an azeotrope. Specifically, the pitfalls in treating the differentials in the Gibbs-Duhem equations as variations are demonstrated. The critical role played by the rank of a submatrix in the coefficient matrix of the Gibbs-Duhem equations is highlighted. A hierarchy in the application of the phase rule is pointed out and the need for a unified framework for interpreting the phase rule is indicated. © 2012 Elsevier Ltd.
Coulson and richardson’s chemical engineering
Coulson and Richardson’s Chemical Engineering: Volume 3A: Chemical and Biochemical Reactors and Reaction Engineering, Fourth Edition, covers reactor design, flow modelling, gas-liquid and gas-solid reactions and reactors.
A hierarchy of transport models motivated by studies of the Stefan tube
Motivated by studies of the diffusion of a gas mixture in a Stefan tube, we present a hierarchy of mass transfer models with the species momentum balance and the species continuity equations as the basis. The simplifying conditions and the constitutive equations that lead to the equations of the mixture momentum balance approach are obtained. Further, the form that these equations should take for a multicomponent mixture is derived. These equations are shown to be a generalization of the Meyer–Kostin equations used to study binary diffusion in a Stefan tube. Additional simplifications that result in the so called classic approach to diffusion are identified.
Toward a unified framework for interpreting the phase rule
The apparent differences in the statements of the phase rule for the two sets of variables commonly used, namely, temperature, pressure, and mole fractions on the one hand and temperature, pressure, and chemical potentials on the other are resolved by developing a framework in which the phase rule may be stated and analyzed in terms of a whole class of variable sets. The framework is restricted to the case where all the components are present in all the phases. Central to the framework is the notion, due to Gibbs, of a fundamental relation for homogeneous states and the associated general equation cast in terms of intensive and specific variables. The significance of the Gibbs-Duhem equations within the context of the phase rule is brought out. The lead provided by Gibbs in his approach to the phase rule is utilized to carry out a local analysis of the equations that result from the criteria of equilibrium for the two sets of variables referred to above. The central role played by the general equations is brought out. The scope of the phase rule is widened by identifying particular sets of variables that would be suitable for uniquely defining the equilibrium state of a multiphase mixture. © 2012 American Chemical Society.
Critical analysis of maxwell's equal area rule: Implications for phase equilibrium calculations
The fundamental flaws inherent in Maxwell's equal area rule are analyzed. Using an alternative principle that overcomes the limitations of Maxwell's rule, general equations are derived for determining the saturation pressure and other properties associated with the liquid-vapor phase transition given an arbitrary equation of state. The equivalence of the equation for saturation pressure to those available in the literature is proved. It is found that the alternative principle predicts saturation pressures that are significantly different from those calculated using Maxwell's rule. These results are based on numerical studies on three different equations of state and fifteen substances. Similar results are obtained for the vaporization entropy as well. © 2010 American Chemical Society.